I think that is an incredibly simplified view of switching to a whole-food diet. While it is arguably better to consume whole-foods as opposed to processed foods, that isn't a cure-all. Additionally, it kind of dismisses the existence of the availability of whole-foods for low-income, under-privileged communities. If someone lives in a food desert, they don't necessarily have the option to chose unprocessed foods, or if they did, the time to prepare whole meals.
And just to throw this out there: in many states that have subsidized health-care, it can be more accessible to low-income communities, as opposed to more expensive, not readily available groceries.
Pollan may have addressed this, but comments like that tend to overlook income inequality and equal access to food/grocery stores.